2y^{''}+3y^'+5y=3cos(5t)

Lösung

2 y^{^{''}} + 3 y^{^{'}} + 5 y = 3 cos (5 t)

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{31 t}{4}) + c_{2} sin (\frac{31 t}{4})) + \frac{1}{50} sin (5 t) - \frac{3}{50} cos (5 t)

Schritte zur Lösung

2 y^{''} (t) + 3 y^{'} (t) + 5 y = 3 cos (5 t)

Solve linear ODE:

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{31 t}{4}) + c_{2} sin (\frac{31 t}{4})) + \frac{1}{50} sin (5 t) - \frac{3}{50} cos (5 t)

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{31 t}{4}) + c_{2} sin (\frac{31 t}{4})) + \frac{1}{50} sin (5 t) - \frac{3}{50} cos (5 t)

y^{^{''}} + 25 y = 4 cos (5 x) + 6 sin (5 x)

y^{^{''}} + 4 y - 4 = 0

y^{^{''}} + 2 y^{^{'}} + y = sin (t)

y^{^{''}} - 8 y^{^{'}} + 16 y = 12 e^{4 x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 3 e^{- 3 x} - e^{- x}